Let \(M\)  be a maximal subgroup of \(G\)  such that \(\operatorname{Soc}(G/M_G)\)  is \(G\) -isomorphic to \(A\) . We have that \(\operatorname{Soc}(G/M_G)=C/M_G\)  and \(R\le M_G\le C\) . Moreover, there exists an isomorphism \(\varphi \colon G/M_G\longrightarrow L\)  satisfying that the composition with the projection over \(G/C\) , \(G/M_G\longrightarrow L\longrightarrow G/C\) , has kernel \(C\)  and gives he identity on \(G/C\) . Let us now give a bound for the number of possible kernels of epimorphisms from \(L_K\)  to \(L\)  giving the identity on \(G/C\) . By [1]}, the number of possible kernels of epimorphisms from \(L_k\)  onto \(L\)  giving the identity on \(G/C\)  is \((q^k-1)/(q-1)\) . By Equation (REF ),
\(\frac{q^k-1}{q-1}\le \frac{\frac{n^{d-1}}{\vert \operatorname{H}^1(L/A,A)\vert }-1}{q-1}=\frac{n^{d-1}-\vert \operatorname{H}^1(L/A,A)\vert }{(q-1)\vert \operatorname{H}^1(L/A, A)\vert }.\) 
